Question: A car of mass 1000 kg is moving with a constant speed of 20 m/s on a straight
horizontal road with an output power of 20 kW. I f the output power is suddenly increased to
60 kW, what is the acceleration of the car at this instant?
Solution:
𝐴 𝐹∙𝑆
=
= 𝐹 ∙ 𝑉, 𝑤ℎ𝑒𝑟𝑒
𝑡
𝑡
𝐴 − 𝑤𝑜𝑟𝑘,
𝑡 − 𝑡𝑖𝑚𝑒,
𝐹 − 𝑓𝑜𝑟𝑐𝑒,
𝑉 − 𝑠𝑝𝑒𝑒𝑑.
𝑚
𝑃1 = 20000 𝑊,
𝑉1 = 20
𝑠
𝑃2 = 60000 𝑊
𝑇ℎ𝑒 𝑓𝑖𝑟𝑠𝑡 𝑝𝑜𝑤𝑒𝑟 𝑖𝑠:
𝑃1 = 𝐹 ∙ 𝑉1
𝐹 = 1000 𝑁
𝑇ℎ𝑒 𝑠𝑒𝑐𝑜𝑛𝑑 𝑠𝑝𝑒𝑒𝑑:
𝑃2
𝑉2 =
𝐹
60000
𝑚
𝑉2 =
= 60
1000
𝑠
∆𝐴
∆𝑃 =
𝑡
Time is:
𝑚 ∙ (∆𝑉)2
∆𝐴
2
𝑡=
=
= 20 𝑠,
∆𝑃
∆𝑃
𝑤ℎ𝑒𝑟𝑒
𝑚 − 𝑚𝑎𝑠𝑠 𝑜𝑓 𝑐𝑎𝑟,
∆𝑉 = (𝑉2 − 𝑉1 ),
∆𝑃 = (𝑃2 − 𝑃1 ).
𝑃=
𝑨𝑵𝑺𝑾𝑬𝑹:
∆𝑉 40
𝑎=
=
= 2 𝑚/𝑠 2
𝑡
20